Apparatus for generating involutes



Oct. 14, 1958 Filed Dec. 21, 1954 H. HOFER 2,855,678

APPARATUS FOR GENERATING INVOLUTES 3 Sheets-Sheet 1 Oct. 14, 1958. H.HOFER APPARATUS FOR GENERATING INVOLUTES Filed Dec. 21, 1954 5Sheets-Sheet 2 ATTORNEKS Oct. 14, 1958 I HOFER 2,855,678

7 v APPARATUS FOR GENERATING INVOLUTES Filed Dec. 21, 1954 5Sheets-Sheet 3 7 7 I ILfiIIIIIIE-U 1555355555515 INVENTOR I .E j IATTORNEY United States Patent O APPARATUS FOR GENERATING INVOLUTESHermann Hofer, Friedrichshafen, Germany, assignor to ZahnradfabrikFriedrichshafen, Friedrichshafen A. B., Germany Application December 21,1954, Serial No. 476,801

Claims priority, application Germany December 23, 1953 12 Claims. (Cl.33--27) The present invention relates generally to mechanisms forgenerating geometric curves and more particularly to a mechanism for thedirect generating of involute curves.

The object of the invention is to provide an inexpensive mechanism whichis simple in construction and containing a minimum number of parts bywhich involute curves may be accurately and quickly generated upon aworking surface.

Another object of the invention is the provision of adjustable elementsin the mechanism whereby involute curves corresponding to variousdiameter base circles may be accurately generated with a simple movementon a working surface using only a single roller arc.

Other objects and advantages, in part, will be obvious, and :in partpointed out hereinafter during the course of the following description:

The invention accordingly resides in the combination of elements,features of construction and arrangement of parts. The scope of theinvention will be more fully set forth in the claims at the end of thisspecification.

For a more ready comprehension of this invention, reference is had tothe accompanying drawings, wherein:

Fig. l is a plan view of the invention.

Fig. 2 is a side view of the invention, viewed substantially indirection 22 of Fig. 1.

Fig. 3 is a sectional View taken substantially along line 3-3 of Fig. lwith an accompanying side view of the drawing board.

Fig. 4 is a sectional view taken substantially along line 4-4 of Fig. 1with the carriage in its zero position where the involute angle equalszero.

Fig. 5 is an enlarged sectional view taken substan tially along line 5-5of Fig. 4 showing the mounting of the graduated rule.

Fig. 6 is a sectional longitudinal view of a modification of theinvention embodying a movable drawing board.

Fig. 7 is a sectional view of the modification of the invention takensubstantially along line 7-7 of Fig. 6.

Fig. 8 is a sectional view similar to Fig. 7 of the modification of theinvention with some of the parts removed to show the invention in anadjusted position.

Like reference characters refer to like parts throughout the severalviews of the drawing.

As conducive to a clearer understanding of certain features of theinvention, it may be noted at this point that an involute curve isdefined as being the path of any point on a tangent to a curve thatrolls without sliding around the curve. In the past the involute curvehas found widespread application in design work. One example of such anapplication is in the design of gears where the gear teeth are ofinvolute curvature. The involute curvature of gear teeth has a circulargenerating curve. In practice the base circle of the gear is used as thegenerating curve upon which a tangent is in efiect 'rotated withoutsliding.

The usual well known methods for constructing inyollltc curves such asthe point by point layout method,

ice

the use of templates, or the unwinding or winding of a taut string fromor on the surface of a cylinder require lengthy and involved operations,and any of these methods are subject to errors. Various instruments havebeen proposed to generate involute curves but they have been complicatedand expensive and also not particularly beneficial from the standpointof accuracy.

It is therefore the outstanding object of this invention to provide aninvolute generating mechanism both light and simple and characterized bya high degree of accuracy that will produce with a single rolling arc aninvolute curve from an infinite number of various diameter base circleswithin its range of operation.

As specifically illustrative of the practice of this invention, Fig. 1illustrates an involute curve generating mechanism inscribing aninvolute curve. There is utilized a stationary semi-circular drawingboard or disc 10 which has a center point designated by a pin 11.Adjacent the board 10 there is arranged a straight rail or tangentelement 12 which is adapted to roll around the outer periphery of theboard 10 without sliding. The rolling movement of the rail 12 is securedby two bands or strips 13 and 13 located around the outer periphery ofthe board 10 and secured to it by means of screws 14 and 14respectively. The opposite ends of the strips 13 and 13' are fixed tothe rail 12 by means of screws 15 and 15 respectively. The strips orbands may be of any flexible material such as metal or plastic in orderthat a smooth surface be provided. In order that the rail 12 rolls ofiperfectly on board 10 I provide recesses 16 and 16' at the upper andlower portion of the board edge as shown in Fig. 3. The bands 13 and 13fit within these recesses and have a thickness less than the depth ofthe recesses to insure continuous tangential contact between the boardand rail. The rail 12 is provided with an extension or side rail 17connected thereto in a fixed manner which laps over the upper surface ofthe board 10 (see Fig. 3).

As shown in Fig. 1, there is provided a pivoted lever serving as a guiderail 18 containing a centrally located slot 19 constituting alongitudinal guideway. At the lower end of the slot, pin 11 is located,around which the rail pivots. On the straight rail 12 a stationary pin20 is provided and projects through the slot 19 also and serves as afollower. When the rail is moved around the edge of the board the pin2%) slides longitudinally within the slot 19 while the guide rail 18pivots around pin 11. On the upper side of the extension 17 there isprovided a shallow groove 21 as seen in Fig. 2 and Fig. 3 constituting alongitudinal guideway. This groove receives a pair of wheels 22, 22'which form parts of a carriage 23 and being supported in spacedrelationship on extensions 24, 24' fixed to a rigid crossbar orconnecting member 25. The crossbar 25 contains a central passage 26arranged to receive a slide in the form of a graduated rule 27. Thisrule is adjustably positioned with respect to the carriage 23 and isrigidly maintained in the desired position by means of threaded screw 28mounted in a housing 29 attached to the carriage. The housing 29 isrecessed longitudinally at 30 to receive the rule 27. A plate 31 securedby means of screws 32, 32 to the housing retains the slide within therecess. When the screw 28 is screwed down its lower end contacts therule 27 and secures it in fixed position.

At the end of the rule 27 there is located a curve describing instrumentsuch as a downwardly depending scribing point 33 which rides in the slot19 and inscribes the involute curve on the surface of the board as theguide rail 18 pivots.

In the operation of this mechanism the material or paper upon which thedesired involute curve is to be reproduced is attached to the board 10.The basic circle around which my mechanism operates is the circle formedby the edge of the drawing board containing a radius Rg and acenterpoint defined by pin 11. An involute is described by themovementof pin 20 as the rail ll is rolled around the board 10 without slidingin continuous tangential contact. I The cusp of such an involute curveat the base circle is F It can be seen that the writing element 33 as itmoves within the slot 19 will always lie on the same'radial line as thepin.20 and since the rule 27 is always maintained perpendicular to thetangential rail 12 a line through point 33 parallel to rail 12 willbe incontinuous tangential relationship with a base circle having a diameterrg. This diameter therefore would depend on the distance (a) between thepoint 33 and the tangential rail 12. The involute therefore inscribed bywriting element 33 would have a cusp (R) from its base circle. Itwill benoted that the mechanism can be operated in'either direction orrotation. Therefore an involute curve with a cusp (f on the base circlecan be drawn in either a clockwise or counter-clockwise direction asshown by the arrows in Fig. 1.

The rule can be provided with a graduation scale in order to provide fora ready selection of the distance (a) and consequently the base circlediameter of the drawn involute curve. The operation of the mechanism ispractically automatic as the operator need only grasp the rail 12 or 18and with a single rotary movement the selected involute curve isreproduced.

If it is desired to obtain the involute angle an angle scale may beattached to the board 10. As shown in Fig. 1 the involute angle a wouldbe the dilference between angle }8 and angle g0. Angle ,8 would be theangle formed by the two lines taken from pin 11, the base circle center,one to the point of tangential contact of bands 13 and 13' and the otherthrough points of origin F and f of the involute curve. Angle 0 would bethe angle formed by the two lines taken from pin 11, as shown on Fig. 1.

Figures 6, 7 and 8 illustrate a modification of the invention wherein amovable drawing board or base disc 50 in the form of a circular segmentis utilized instead of a fixed drawing board. The drawing board ismounted on a base or ground plate 51 and rolls ofi without sliding withits arcuate edge on a solid rolling line fixed to the base plate.

The rolling oif movement can be secured through a wire having ends 52,52' and a back section 53 tensioned over two fixed rollers or plugs 54and 54. One end 52' of the wire lies against the arcuate surface ofboard 50 as shown in Fig. 6 and is fastened thereto by screw 55'.

The other extremeity 52 of the wire also runs along the arcuate edge ofboard 50 and is connected to the board by screw 55. The wire may beconsidered a stationary tangent element relative disk 50 although it hasmotion to drive a curve describing element.

In base plate 51 clamping pin 56 is located and the back section 53 ofthe wire passes through the pin shank. By means of a screw 57 7 carriedby the pin the roll off wire can be fixed in the drawing position.

Within the base plate 51 a shallow guide groove 58 is provided in whicha pin or bolt 59 fixed to board 50 slides. The lower end of the guidepin 59 is cylindrical and of somewhat smaller diameter than the width ofthe groove 58. Therefore when rolling oif the board 50 on a rolling linethe center of the rolling circle formed by the board moves on a lineparallel to the rolling line. The pin 59 serves simultaneously as arotation pin for rail or lever 60.

' Mounted directly over the drawing board as shown in Fig.6 a guide rail60 is provided having on its underside a rectangular groove 61constituting a longitudinal guideway. A stirrup member 62 is fixed toone side of the baseplate 51 and contains an extension 63 on which afixed pin or follower 64 is supported. This fixed .4 pin is arranged toslide freely in the rail groove 61 and lies above the rolling lineformed by the wire ends 52, 52 as shown in Fig. 7.

The base plate 51 is provided with another groove 65 constituting alongitudinal guideway which runs parallel appropriately with inclinedside walls. As shown in Fig. 6 a carriage 66 provided with a pair ofrollers 67, 67" mounted within holes 68, 68 of the carriage moves bymeans of the rollers in the groove 65. The rolling surface of therollers is conical and shaped to fit the form of the groove 65.

The carriage 66 is provided with an arm 69 or bar which carries awriting element 70. The writing element 70 is positioned in a guide orslide 71 which is a curve describing instrument and is fixed adjustablyalong the arm 69 by screw 72. In addition guide 71 has a guide pin 73which slides in the rectangular groove 61 and lies on the sameaxis aswriting element 70. Pin 64 and guide pin 73 are formed correspondinglyconical and slide on the lower edges of the rectangular groove 61.

In order to equalize the weight of the carriage 66, the U-shaped portionof the carriage which lies to the right of the rollers 67, 67 in Fig. 6,is made of steel and the arm 69 is made of light metal. Therefore thewriting element 70 presses equally and only lightly on the paper in allpositions.

In the operation of the device pin 59 is pushed against and guided alongthe surface of groove 58 facing the rolling ofi side of the board 50. Inthis longitudinal movement the drawing board 50 with its arcuate surfacerolls off on the rolling line of wire 52, 52'. During this operationrail 60 rotates around pin 59 and is guided at its face end by means ofthe fixed pin 64 in groove '61. At the same time carriage 66 is movedsidewise by means of the pin 73 and rolls in groove 65. Pin 73 of theguide 71 is guided in groove 61 and writing element 70 draws theinvolutes indicated in Fig. 7 at e e and e;;.

It will be noted that the plumb line as shown in Fig. 7 which is createdon the rolling line by fixed point 64 is also the symmetrical axis ofthe drawing board 50. The base points of the involutes e e and eg, etc.,drawn in this position of the drawing'board lie also-on the center axisof the board. The involutes can be drawnin either direction from thebase points depending on the direction of movement of pin 59. a

If it is desired the screw 57 can be loosened and the wire 52, 52' 53can be displaced by rotating board 50 around pin 59-which is held fast.The screw '57 is subsequently tightened again. The plumb lineestablished on the rolling line through the fixed pin 64 is nowdisplaced by the angle AE form the symmetrical axis of the board 50 asshown in Fig. 8. Therefore another plurality of involutes e e e etc.,can be drawn, the base points of which lie on a new zero axis.

Along the wire section 53 adjacent the groove 65 a longitudinal scale 74is printed on the base plate 51. Along the wire 53 above the scale amark 75' is attached which indicates the desired amount of displacementof the wire. This scale can be calibrated in units of the center angle.The mark 75 is opposite the zero point of the scale when the axis ofsymmetry of the board 50 lies on the plumb line through the pin 64.

If it is desired a perfect operation of the rolling off device can beobtained by eliminating the wire 52, 52', 53 and groove 58. Instead asimple, smooth, tangential rule is fixed on the base plate 51 in placeof the wire against which the arcuate edge of the drawing-board 50 rollsoff without further auxiliary means merely by pressing against thetangential rule. The necessarycourse of the rolling 0E movement (withoutsliding) is obtained here by the contact friction of the two rollingsurfaces against each other.

As will be readily seen, I provide a simple and inexpensive mechanism bywhich a wide variety of involute curves maybe quickly and-accuratelygeneratedby effecting a simple adjustment and previously developedinvolute curves may be readily checked. Furthermore the desired involutemay be generated in one direction or the other with respect to the basecircle without modification or adjustment of the apparatus. I

It is apparent from the foregoing that once the broad aspects of theinvention are disclosed, many embodiments thereof and many modes ofapplication all falling within the scope thereof, will readily occur tothose skilled in the art. Moreover, many modifications of the particularembodiment herein disclosed will likewise suggest themselves.Accordingly, the invention is intended to be limited only by the scopeof the following claims and the foregoing disclosure is made solely byway of illustration.

I claim:

1, A mechanism for generating involutes comprising a circular base disc,a rotatable lever pivoted at the center of said disc, a tangent elementrolling tangentially without slipping on said disc, a follower connectedto said tangent element, said follower engaging said lever and movablealong said lever, a carriage slidably connected to said tangent elementfor longitudinal movement therealong, a slide adjustably positioned onsaid carriage and extending perpendicular to the direction of movementof said carriage, said slide containing a point engaging said lever andslidable along said lever to generate involute curves of various basecircle diameters according to position of said slide, when said tangentelement is rolled on said disc.

2. A mechanism for generating involutes comprising a circular base disc,a rotatable lever pivoted at the center of said disc, a tangent elementrolling tangentially without slipping on said disc, a follower on saidtangent element engaging said lever and movable longitudinally alongsaid lever, a carriage slidably connected to said tangent element forlongitudinal movement therealong, a slide adjustably positioned on saidcarriage and perpendicular to the direction of motion thereof, saidslide containing a point engaging said lever and slidable along saidlever to generate both branches of involute curves of various basecircle diameters in either direction of rolling of said tangent elementon said disc.

3. A mechanism for generating involutes comprising a circular base disc,a rotatable lever containing a central longitudinal slot and pivoted atthe center of said disc, a tangent element movable tangentially on theperiphery of said disc without slipping, a follower on said tangentelement slidable within said lever slot, a carriage slidaby connected tosaid tangent element for longitudinal movement therealong, a slideadjustably positioned on said carriage and perpendicular to thedirection of motion thereof, said slide containing a point also slidablewithin said lever slot to generate both branches of involute curves ofvarious base circle diameters according to position of said slide whensaid tangent element is rolled in either direction on said disc.

4. A mechanism for generating involutes comprising a circular base disc,a rotatable lever pivoted at the center of said disc, a tangent elementrolling tangentially relative to said disc without slipping, andcontaining a follower engaging said lever and movable along said lever,a carriage slidably connected to said tangent element for longitudinalmovement therealong, a bar fixed on said carriage and extendingperpendicular to the direction of motion of said carriage, a slideadjustably positioned on said bar and containing a point also slidablealong said lever to generate both branches of involute curves of variousbase circle diameters according to the position of said slide, when saidtangent element is rolled in either direction on said circular disc.

5. A mechanism for generating involutes comprising a circular base disc,a rotatable lever containing a central longitudinal groove and pivotedat the center of said disc, a stationary tangent element, said circularbase disc rolling on said tangent element, a follower incorporated insaid tangent element and engaging said groove of said lever, a carriageslidably connected to said tangent element for longitudinal movementtherealong, a bar fixed on said carriage and extending perpendicular tothe direction of movement of said carriage, a slide adjustablypositioned on said bar and containing a point also slidable within thegroove of said lever to generate both branches of involute curves ofvarious base circular diameters according to the position of said slide,when said disc is rolled in ,either direction on said tangent element.

6. A mechanism for generating involutes comprising a circular base disc,a rotatable lever having a longitudinal slot and pivoted at the centerof said disc, a tangent element movable tangentially without slidingrelative to the periphery of said disc, and having a longitudinalgroove, a follower on said tangent element slidable along said leverslot, a carriage supported by a pair of rollers maintained in spacedapart relationship, a connecting member for maintaining saidrelationships, said rollers rolling within said groove, a slideadjustably positioned on said connecting member for adjustmentperpendicular thereto, said slide containing an element also slidablealong said lever slot to generate both branches of involute curves ofvarious base circles when said tangent element is rolled in eitherdirection on said disc.

7. A mechanism for generating involutes, comprising a circular basedisc, a rotatable lever containing a central longitudinal groove andpivoted at center of said disc, a ground plate carrying said disc, twoplugs secured to said plate, a wire stretched around said plugs, theopposite end pieces of said wire crossing each other and embracing saiddisc and said wire extending linearly in opposite directions from thecrossover point, and the ends of said wire secured to said disc, agroove provided in said ground plate and parallel to the centerline ofsaid plugs, a bolt at the center of said disc engaging said groove insaid ground plate and adapted to be guided manually in said groove, saiddisc being adapted to roll on the linear length of said wire in eitherdirection from said crossover point, a follower incorporated in saidground plate, the vertical axis of said follower being in the plane ofsaid center-line, said follower engaging said groove of said lever, acarriage slidably connected to said ground plate for movement parallelto said centerline, a bar fixed on said carriage and extendingperpendicular to said center-line, a slide adjustably positioned on saidbar and containing a point also slidable within said groove of saidlever and adapted to generate both branches of involute curves ofvarious base circle diameters according to position of said slide, whensaid bolt at center of said disc is guided in either direction withinsaid groove in said ground plate.

8. The apparatus according to claim 7 in which the bar of said carriageis provided with graduations by which the base circle diameter of thegenerated involute curve can be selectively predetermined.

9. The apparatus according to claim 1 in which the circular base disccontains an angle scale by which the involute angle may be determined.

10. The apparatus according to claim 7, in which said wire is adjustablealong said center-line.

11. The apparatus according to claim 7, in which the ground plate isprovided with graduations, said wire carrying a mark sliding along saidgraduations in order that the position of the wire along its center-linemay be selectively predetermined.

12. A mechanism for generating involutes comprising a segment of acircular disc, a rotatable lever having a longitudinal guideway, andpivoted at the center of said disc segment, a tangent element movabletangentially without sliding relative the segment periphery and having alongitudinal guide means, a follower on said tangent element slidablealong said lever guide means, carriage means guided in the direction ofsaid longitudinal guideway of said tangent element, a curve describingelement, means for supporting said element for translation with saidcarriage in the direction of said guide means of 7 said tangent element,means for adjusting said element References Cited in'the file of thispatent reletive said carriage alonga line normal to the direction UNITEDSTATES PATENTS of travel of said carriage, means on said elementslidable 1 606 0 Fellows Nov 9 1926 along the ay of said rotatable leverwhereby said 401 Bradner 1954 element cribes an involute when saidtangent element and' said segment of the disc are moved relative eachFOREIGN PATENTS other. 534,650 France Jan. 9, 1922

